Well, what you call truths I call Abstractions and the parameters can be anything we choose — Mark Nyquist

No one our earth has ever seen a physically perfect triangle (because perfectly straight lines are impossible in our universe as far as I'm aware). Yet we know that the angels in a triangle add up to 180 degrees. What I'm trying to say with this example is that the parameters cannot be anything we choose. If what we choose or say is contradictory (such as triangles have four sides or one can count to infinity) we cannot meaningfully/rationally say it. As for what determines what's meaningful/rational and what's not, I believe that is Existence. If x is true of Existence, it is rational/meaningful (for example triangles have three sides is true of Existence). If x is contradictory or not true of Existence (such as one can count to infinity), it is not true of Existence (as in the nature of Existence is not such that triangles have four sides or that one can count to infinity).

I don't understand the notation you have used. If you were to put it into words, I could reply in kind.

It seems possible to map a smaller infinity, one to one, on a larger infinity simply by freezing the larger infinity and letting the smaller one catch up. — Mark Nyquist

Whilst I believe it's possible for two different things to go on forever, I don't believe it's possible to have two different sized infinities because even if the two things (such as two number sequences) go on forever, infinity will not be reached (we cannot count to infinity). So when you say "freeze the larger infinity" I assume you mean something like stopping it from continuing to go on forever. But my whole argument is that if something goes on forever, it does not make it infinite precisely because one cannot count or expand to infinity.

Since we set imaginary parameters anything goes. This is not based on anything physical at all. — Mark Nyquist

Some things are imaginary, but some things are truths about the nature of Existence/Being (such as triangles have three sides or one cannot count to infinity).

How would you respond to this:

How would a difference in size be established between two infinite sets when there is no counting involved? And if there is counting involved, how would infinity be reached given that one cannot count to infinity?

but i do not think they are equal in terms of magnitude or value — punos

Suppose two things are travelling at two different speeds. One is faster than the other. Both are set to go on forever. Would you say something like the value of the faster one is greater than the value of the slower one in terms of distance covered? Or would you say they are both of equal value? Or would you say both are set to go on forever but neither will reach an infinite amount of distance covered and so one will have travelled farther than the other if a measurement was to be taken of how much distance it has covered in comparison to the other.

And yet Cantor. — Banno

You do not consider the possibility that Cantor is wrong?

Suppose someone brought proof. How will you recognise it?

If you're trying to argue that a "correct" set theory must allow for a universal set then I don't think you really understand mathematics. — Michael

I believe I understand Russell's paradox very well, but I am not a mathematician.

↪Philosopher19 ZFC is, I believe, set up specifically so that "a list can't list itself". That's how it avoids the various paradoxes. — Banno

But you don't solve a paradox or contradiction by seeking refuge in another.

It is more damning/problematic to reject the set of all sets than to accept ZFC, but any statement, belief, or theory that has a contradiction in it, is wrong by definition.

In any case, I believe I presented a true solution to Russell's paradox. The full writing is here if you are interested:

http://godisallthatmatters.com/2021/05/22/the-solution-to-russells-paradox-and-the-absurdity-of-more-than-one-infinity/

I'd say it's not just incomplete. It's contradictory in the sense that it logically implies "a list can't list itself". That's like saying a shape can't be a triangle (which is contradictory because a shape can be a triangle).

In Zermelo–Fraenkel set theory the axiom of regularity rules out a set being a member of itself. — Banno

That's like saying a list can't list itself. Is this in itself not enough to conclude that the Z-F set theory is inadequate/incomplete?

Yes. But a set, by definition, cannot contain itself — Fire Ologist

I think I understand where you're coming from. I agree that something cannot be the container of itself in the way that you mean "container of itself". But I see a meaningful difference between something being a member of itself, and something containing itself in the way that you mean. To highlight this difference to you, consider the following:

I make a list of all things in my room. The list is in my room so I list the list in the list. This is clearly meaningful is it not? The list meaningfully lists itself does it not? This is what I mean by contain itself (as in in the sense of being a member of itself). Not in the sense of a box that contains a box which is itself.

Agree, but wouldn't it also, in a naive sense, have to also be finite, because it is now an "encompassing" container? — Fire Ologist

I don't think it follows that because x is encompassing, x is finite. If everything is in the Infinite, this does not mean that there is an end to the Infinite, but it does mean the Infinite encompasses all things.

Or I guess I'm now saying a set of infinite, ever-increasing members, never gets to be a set — Fire Ologist

If something (like a number sequence) goes no forever, it does not mean that it reaches infinity or that it is an infinite set/sequence. Does it reach infinity for it to be classed as an infinite set? Can we count to infinity to say it reaches infinity to be classed as an infinite set? So we cannot say 1, 2, 3 ad infinitum is an infinite set, precisely because infinity will not be reached for it to be classed as an infinite set.

There is no beyond infinity. Infinity is complete. It is precisely because Infinity is Infinite that something can go on forever or increase increasingly. But again, this does not make it Infinite/Complete. It just means it's a part of the Infinite/Complete.

If all sets are contained in the set of all sets (that are not members of themselves and nothing more), — Fire Ologist

But I am not saying this. I am saying the set of all sets semantically/logically/rationally contains all sets and it is a member of itself (because it is itself a set). So the set of all sets consists of one set that is a member of itself (itself) and many sets that are not members of themselves (all sets other than the set of all sets). Where is the paradox in this?

Consider semantics. We did not create or make up the semantic that something can be a member of itself or a member of other than itself (or that triangles are triangular or that the set of all sets encompasses all sets). We are aware that such is the nature of Existence (that triangles are triangular and that the set of all sets encompasses all sets) and have expressed awareness of it. The contradiction lies in wanting a set that contains all sets that are not members of themselves that is itself not a member of itself (which appears to be the set that Russell was talking about when he asked is the set of all sets that are not members of themselves a member of itself or not). Such a thing is by definition, contradictory.

we are defining what all sets are. In a logical sense, we are still creating a set that can't be a member of itself, but at the same time is a member of itself. — Fire Ologist

Crack it open again. What is a set? A set is a form of "all". — Fire Ologist

the "all of all alls" — Fire Ologist

I don't see anything wrong with the "all of all alls". You have alls of various sizes with one all encompassing absolutely all alls. By definition, this all that contains absolutely all alls has to be infinite.

That's exactly what Russell was proving. — Michael

So let's say he proved you could not have a set that contains all sets that are not members of themselves and nothing more.

Did he prove that the set of all sets is contradictory?
Did he prove that you could not have a set that contains all sets that are not members of themselves? Because by definition/logic, the set of all sets contains all sets that are not members of themselves (as well as itself).

If Russell proved anything, it's that you can't create a new set that contains absolutely all sets that are not members of themselves and nothing more.

Again, the set of all sets contains absolutely all sets that are not members of themselves as well as itself.

To my understanding, the subset issue was because you could have a set of all sets that are members of themselves. Since you could have this you should also have been able to have a set of all sets that are not members of themselves so that there are no inconsistencies in the subset level. I have shown that you cannot have a set of all sets that are members of themselves.

Wanting to have a set of all sets that are not members of themselves that is itself not a member of itself is a contradictory thing to want.

Only the set of all sets can contain all sets that are not members of themselves precisely because all sets are members of it and not themselves (of course it is a member of itself)

My full writing on Russell's paradox can be found here if interested:

http://godisallthatmatters.com/2021/05/22/the-solution-to-russells-paradox-and-the-absurdity-of-more-than-one-infinity/

Consider the following two lists:

The list of all lists (Call this L)
The list of all lists that list themselves (Call this LL)

Both the above lists list themselves (put differently, both lists are members of themselves).

Importantly, they are only members of themselves in their own respective lists. As in the list of all lists only lists itself in the list of all lists (L is only a member of itself in L). It does not list itself in the list of all lists that list themselves (L is not a member of L/itself in LL precisely because it is a member of LL).

The point I'm trying to make:

You cannot have a set of all sets that are members of themselves with all its members actually being members of themselves whilst they are members of it.

This should resolve the subset issue and we should no longer contradictorily say "the set of all sets is contradictory".

I feel the only way to escape this paradox is to say that we are designed by some higher truth in the universe. — Franz Liszt

Science is an empirical matter. It's something that is not 100% and is open to interpretation (like scripture). Something like triangles have three sides, is a matter of pure reason. This is 100% and is not open to interpretation. Matters of pure reason cannot be meaningfully/semantically refuted.

If you want something 100% or rational with regards to the nature of existence, I recommend the following:

https://thephilosophyforum.com/discussion/11100/god-as-the-true-cogito/p1

Dear 3017amen

As a Christian Existentialist, Revelation has always told me that the concept of a God is something beyond logic and pure reason, — 3017amen

I disagree with this point. There is no beyond logic and reason. There is rational and irrational; logical and illogical; truth and falsehood. However, you can say that there are unknowns to non-Omniscient beings such as us. This is not the same as saying there are things beyond logic and pure reason. The statement "there are things beyond logic and pure reason" is as contradictory/irrational as "there are more triangular things than perfect triangles". Any given belief or statement that is contradictory or irrational, is wrong by definition.

With regards to why God's existence is indubitable, I recommend the following:

https://thephilosophyforum.com/discussion/11100/god-as-the-true-cogito/p1

With sincerity to God/Truth/Goodness,
Nyma Bakhshayesh

wish you much success with it. It is probably very difficult to establish new ideas against the spirit of the times, especially regarding proofs of God. Here is an appropriate quote from a German philosopher, which I have also translated: — spirit-salamander

Thank you, and thank you for that which you translated and shared. It was good to read about the writer's interpretation of the attitudes of the western world towards an ontological argument.

I am also no exception, with me reservations, resistances and prejudices are instinctively given against proofs of God. — spirit-salamander

I appreciate the honesty. I lived with the belief that existence is perfect since around 2013. But it wasn't until around 2018 that I really, genuinely, and sincerely committed to this premise. When I did, the empirical evidence for Karma being absolute, full, and extensive, was overwhelming. Again, this was something that I had understood a priori sincere 2013, but did not really empirically embrace because of the way the world looked to me. I thought with all that I hear in the news, there's no way Karma is absolute here. It's probably absolute when Heaven and Hell enter the equation. But my experiences in 2018 and onwards had brought me closer and closer to seeing this clearer posteriori such that I now conclude Karma is absolute. Everyone gets exactly what they truly deserve in this life (and not just in Heaven and Hell).

My point with this is that I discovered whenever I abandoned the a priori because I was to weak to handle the a posteriori (the appearance of things), or because I just had the belief that it can't be this good (because it looked really unlikely from what people would say and the news would report, rather than what I'd actually experience), I felt like I could have received better if I had held onto the a priori better.

My belief is that If you recognise something as being a priori true, then commit to it more strongly than you would commit to anything else. I have come to this belief both from just reflecting on matters of pure reason, and from actual experiences. There is nothing more certain and more reliable than the a priori (or matters of pure reason). It is absolutely the case that one cannot be blamed for refusing to yield to anything other than the a priori, or to their sincerest conception of goodness (though I think the former has more authority than the latter but they lead to the same thing).

Thank you for participating in this discussion. I wish you the all the best for the future.

I will read your blog post in time to understand you better. In addition, I am not a native English speaker, so the discussion is not very easy for me.

Perhaps your version of the ontological proof of God is a successful one. Then you should write a paper and have it published so that it is discussed by the scholars. — spirit-salamander

Your write like a native speaker. I could not tell that you were a non-native English speaker.

I am trying to make it mainstream that the rejection of God's existence is absurd/contradictory/unreasonable. Hopefully I will succeed one day. If I do, it will be because it was perfection for me to succeed. If I don't, it will be because it was not perfection for me to succeed. But given all that I have seen a priori and a posteriori, I strongly believe that I will succeed.

Maybe you're right about what you've said here. But to me it all sounds very much like pantheism, or at least it could apply to pantheism. I don't think, however, that you want to argue pantheistically, do you? — spirit-salamander

A non-pantheistic (or non-omnipresent) view of God (the perfect being) is contradictory. So both monotheism and pantheism are true because there is only one existence (God's existence), and it exists everywhere. This is another way of saying the omnipresent sustains all realities and nothing is more real than Him.

What do you say to the following example:

A shepherd divides his sheep according to the property of the coat color - black and white. He could separate them according to all kinds of characteristics.

But to divide his sheep according to existing and non-existing ones seems abstruse. Therefore, existence is possibly not a property. — spirit-salamander

Yes, but it does not alter the fact that there are things that we can describe as not existing (meaning that they do not have the property of existing) and things that are existing (which must mean they have the property of existing as opposed to not having it). An absolute example of something that does not have the property of existing, is a round square. The absolute example of something that has the property of existing, is God. As highlighted in the OP, God's existence is not susceptible to doubt, whereas ours is. Again, the flaws in Descartes' cogito highlight this.

If we don't deal in absolutes, then it is the case that we meaningfully distinguish between things that exist in different ways (the dream exists as a dream, thus, it has the property of existing first, then the property of being a dream), and things that don't exist at all (round squares, or me standing right now when I'm actually sitting right now). We could not do this (distinguishing between things that exist and things that don't) if existing was not a property.

Also, it might be worth noting that whilst the dream exists as the dream, only one thing exists as existence (or the omnipresent). That thing is God. Everything that exists, does so in existence or because of existence. In other words, everything exists, because existence exists. Only existence exists because it itself exists. Only existence is a member of itself as an existent. Only existence is self-existing or not contingent on anything else whilst everything else is contingent on it. This is why God is the first thing that we should be acknowledging as being truly real or truly existing. This is why only God's existing qualifies as existence in an absolute sense. It's not our existence. It's God's, and we sustained by it.

In general, I agree with you, although in the history of philosophy there has always been a dispute about what is semantically inconsistent and what is not. But keep in mind, some say that there can be no fixed rules for the correct, i.e. absolutely correct use of language. They might say that logic is based on the law of contradiction, but contradiction exists only in words. — spirit-salamander

I studied philosophy at university, and the thing that I notice now that I did not notice as much back then, is that western philosophers do not seem to treat absurdities as absurdities as forcefully as they ought to. By this I mean some will entertain or accept something like Pyrrhonian scepticism as a form of "scepticism" despite it being as contradictory/absurd as something like multishapism "geometry" (mutishapism "geometry" deals with the study of "shapes" like round-squares and triangular pentagons). Any rational person ought to treat that which is absurd as absurd. Unknowns are unknowns (is there is a 10th sense?) and absurdities are absurdities (round squares). This distinction is clear. Thus, our obligations are rationally clear. If we clearly recognise that rejecting belief x is contradictory, then we must acknowledge belief x as certainly true.

There is a theological doctrine or model of God that says that He is a divine simplicity, which means that He has no distinct properties — spirit-salamander

But if this is contradictory, then it is surely false and therefore surely impossible to be real in any way, shape, or form. One is not maximally good in an absolute sense if one is not omnipotent. But clearly, the attributes of omnipotence and goodness are not the same, nor are the attributes of creativeness and infiniteness. If divine simplicity states that they are the same, then divine simplicity is clearly absurd (not meaningful or understandable) and must therefore be rejected.

For our mind such a teaching is contradictory, but nevertheless not necessarily false and impossible. — spirit-salamander

I think this statement is contradictory. We cannot recognise something as being contradictory, yet at the same time, consider it as not being impossible. If x is contradictory, it is certainly impossible. No two different attributes can be the same attribute. No one thing can be two different things at the same time. No x can be not x at the same time. Nothing can sit and stand at the same time etc. These are all clear impossibilities. Whether or not something with a 10th sense exists or not, that is an unknown. Absurdities should be treated as absurdities, and unknowns as unknowns (just as triangles should be treated as triangles, and not as squares).

"For Hegel, all finite concepts are inherently ‘contradictory’ because they are always partial and one-sided and usually derive their meaning from opposed ideas." (The Hegel Dictionary - Glenn Alexander Magee)

"Hegel also often speaks not just of thought as involving contradiction, but reality as well." (The Hegel Dictionary - Glenn Alexander Magee) — spirit-salamander

Contradictions and absurdities and lies exist, what they describe does not. There are no contradictions in reality (this is understandable). Now consider the alternative: There are contradictions in reality (is this understandable for one to say they have meaningful understood it?). One cannot see a round square, and one cannot understand reality as being contradictory.

I'm not sure what example Hegel has produced to justify such a statement, but even if he had, he could not have understood the statement because it would be contradictory.

So there are at least different views on this topic. — spirit-salamander

Yes, but we must not allow ourselves to view a view that is contradictory, as being a reasonable view. The irrational and the rational are not the same. No psychologist or scientist would adopt a clearly contradictory theory (unless they were irrational), yet to my understanding, this is happening in mainstream philosophy and maths (see how mathematicians reject the set of all sets).

What do you mean by meaningful things? — spirit-salamander

I mean anything that is not contradictory or unknown. Round squares do not exist in any way. Unicorns exist at least as hypothetically possible beings. A 10th sense is either an absurdity, or it is at least a hypothetical possibility (we don't know which), but that which is omniscient does.

Existence exists everywhere. Thus, existence (or that which is omnipresent), exists necessarily, as opposed to just a hypothetical possibility. This is because existence (that which is omnipresent) encompasses and sustains all realities and worlds. Unicorns and humans don't have the same ontological necessity as the omnipresent or existence. It is that which perfectly exists that is necessarily absolutely real, whereas unicorns do not perfectly exist, so they are not necessarily absolutely real. They are not perfect beings and there is only one perfect being. That being God.

Because I take the absolute approach, I describe God as instantiating existence, and unicorns as being in existence (as in it is possible for existence to produce and sustain unicorns, but it is not possible for existence to produce and sustain round squares). We must rationally account for why existence is such that round squares are clearly absurd, and why unicorns are not. And the only explanation is that it's just in the nature of existence...that nature being perfect (infinite and omnipotent). A perfect existence accounts for all semantics (including perfection and imperfection, infinite and finite), and imperfect existence cannot account for all semantics (hence why it is contradictory to view existing as finite or imperfect). In an imperfect existence, perfection would be as impossible and absurd as a round square, yet, we recognise that round square is absurd, whilst perfection is clearly meaningful (as is infinity despite us not being infinite). We cannot reject attributing infiniteness and perfectness to existence without running into clear contradictions.

"A hundred real thalers do not contain the least coin more than a hundred possible thalers" (A599/B627, AW 822a). — spirit-salamander

Pretend/imaginary money and real money (real in terms of what we call our waking physical reality) are both in existence. If we take the absolute approach with regards to semantics, then neither the real money or the pretend money are themselves existing because they are sustained by God (which truly exists. Self-exists or is self-contingent). So here, existing or existence is still a property (one that only applies to God).

If we take the non-absolute approach to semantics, then both the pretend money and the real money have the property of existing purely because they are both meaningful. Anything that is absurd (like round-squares) is devoid of the property of existing. Or if I am to put it in the absolute way, is not true of existence. It is not true of existence that it is finite. It is not true of existence that it encompasses round squares in any way, shape, or form. It is true of existence that it can produce unicorns (because existence is infinite. A finite existence cannot accommodate an infinite number of hypothetical possibilities or semantics. And it is contradictory to say x is hypothetically possible and yet not hypothetically possible at the same time. Again, we must account for why unicorn is meaningful, whilst married bachelors are not. I think the conclusion is clear. It's all down to the nature of existence).

I don't think that from your own definition of everything you can clearly and unquestionably prove that God exists. — spirit-salamander

If we take the absolute approach, then only God is existing because God is instantiating existence. We are in existence, but we are not existence because we do not instantiate it. But I recognise the difficulty in saying x does not exist when x is not a contradictory thing. But what the flaws in Descartes' cogito conveys, coupled with what the OP proposes, is that if we are to be certain of the realness or existing of anything, it is God. Everything else could be a dream, or just not truly real. By semantics/reason, God is necessarily existing and real (we are not necessarily real and existing like God is).

I certainly think that definitions contain only concepts of our head, but that our head grasps many things that do not exist. — spirit-salamander

Give me an example. Because if you take the absolute approach, then only God qualifies as really or certainly existing. And if you take the non-absolute approach, then God is the most real existent (see my point about omnipresence encompassing all realities). The concepts in our head are not sustained by us. The concepts in our head do not pop in and out of existence because it is absurd for x to enter existence from non-existence, or to exit existence into non-existence. Thus, we simply access, or focus on one or more of an infinite number of concepts sustained by existence (God's existence to be more precise).

I also agree with Michael Martin's following critique of the ontological proof of God: — spirit-salamander

None of this applies to the OP. Both Descartes and Anselm took existing to be a good thing without justifying this move. I do no such thing. I ask what perfectly exists, and I provide the answer, and that answer is God (or a truly perfect existence). This is different to saying it's better to exist than to not exist, therefore God exists. Given God, if one is evil, it is better to not exist than it is to exist because a truly perfect existence is such that potent evil suffers Hell. God Punishes evil (perfection) and Rewards good (perfection). Clearly, it is better to not exist if one is evil. Or simply, it is better to not exist if one is going to be miserable and depressed, and this will never change. Thus, it's better for evil to not exist. Thus, it is not necessarily the case that existing is a good thing. But it is necessarily the case that existence (that which exists omnipresently) is perfect. Or it is necessarily the case that God is truly real (the omnipresent encompasses all realities).

For example, one can define a Loch Ness monster as a large sea animal that inhabits Loch Ness and define a real Loch Ness monster as a Loch Ness monster that exists in reality. Such a creature would then exist definitionally — spirit-salamander

I can define a visible to my eyes unicorn as existing in my room now. But that definition will not be true of existence because there is no such unicorn in my room. Thus that definition will be contradictory. However, I cannot deny the existence of existence without being contradictory the process. I cannot deny the existence of that which is omnipresent. I cannot deny only God absolutely exists (as demonstrated in the OP). Per the flaws in Descartes' cogito, the following conclusion was established: something is existing (or thinking is occurring as some philosophers say) but it is not necessarily us. Something is existing; as demonstrated in the OP, that thing is necessarily God.

Your appeal to semantic consistency must somehow be supported by something platonically real. — spirit-salamander

Is it not the case that any given theory, belief, or statement that is semantically inconsistent (contradictory) is false by definition? Can you give me an example of something that is contradictory, yet not impossible or false at the same time?

I don't think it's contradictory — spirit-salamander

Is non-existence not devoid of the property of being/existing? Can you give me any thing that is an x, that does not have the property of being an x?

I can say that object X has many color properties and also say that object X exists precisely because I am perceiving it. — spirit-salamander

Right, and if you tried to perceive of a round-square, what happens? You fail because round-squares do not exist in any way, shape, or form. Which means that they do not have the property of existing in any way, shape or form.

You do not say a triangle is not a shape (or does not have the property of being a shape) just because the semantic of 'shape' encompasses the semantic of 'triangle' (as well as all other shapes). The semantic of existing/existence encompasses all meaningful things (including the object X which you perceived). I think you are rejecting the semantic of existence as being a property just because it encompasses ALL meaningful things (shapes included). Not only is there no need to do this, but doing so results in contradictions. I do not think rejecting existence as being a property to be a semantically consistent move.

Before I address any of the other points in your post, I think it most efficient that we clear up this key issue first because everything hinges on this and we have not yet agreed on it.

We'll have to agree to disagree.

And I've read your 'V' stuff before, and I commented on it with exactness. But if you wish to engage me with the additions you've made now, then, to start, you need to clean up the incoherent notation. In a previous post, I suggested how you could do that, but you ignored. — TonesInDeepFreeze

I have no interest in trying to accommodate you any further. What you have said to me and what I have replied to you is clear. I think you have failed to prove your position, whilst I have proved my position left, right, and centre. Evidently you disagree with this.

It's like I said before, we'll have to agree to disagree.

No, you don't. But that is exactly what you are trying to do. — Fooloso4

When I say 'existence' I am referring to that which is omnipresent. Non-existence has never existed and will never exist. You are not existence nor do you sustain it (contrary to solipsism). You are sustained by existence. You are sustained by God. You are contingent on God. Existence = the existence of God and only God. This is when you take semantics in an absolute manner.

If you take semantics in a non-absolute manner, then all meaningful things exist, but only God exists in a real and complete manner. A perfect triangle is really triangular, an imperfect triangle is not really as triangular. The perfect being is really existing, an imperfect being is not as real in its existing. That which is completely/perfectly triangular is at least as triangular as an imperfect triangle. Correction, only that which is completely/perfectly triangular is really triangular in an absolute sense. Nothing else is really triangular. In comparison to God, nothing else is really real/perfect/complete/good.

You do not know that perfect thing exist anywhere but the imagination. — Fooloso4

Then you have not understood the OP. I know that that which exists perfectly exists omnipresently, and I know that only God is omnipresent.

Perfect triangularity is either a hypothesis or part of a formal system. — Fooloso4

The semantic of triangle is the semantic of triangle. Again, if we are to be non-absolute with our semantics, we can talk about varying degrees of triangularity and being. If we are to be absolute with our semantics, then only God (that which perfectly exists) exists, and only triangles (that which is perfectly triangular) are triangular.

But you can have more than one thing that exists. — Fooloso4

Depends on whether you take the absolute approach to semantics or not. If not, then yes, but this does not change the fact that God is more real in its existing than you or any one or any thing/existent else. If you take the absolute approach (which is what you should do), then only God exists. You are just sustained by His existence. It's not your existence or reality (contrary to solipsism), it's God's. You are a part of it.

That is an assertion. You require your perfect, omnipotent God conforms to logic and the limits of your understanding. You seem to be using spatial terms for something that does not have a spatial dimension. — Fooloso4

I am being sincere to my awareness of the semantic of true perfection (of which omnipresence and omnipotence are both semantical components of). If you do not recognise this semantic or are unaware of it, then we cannot discuss it.

I've put effort into understanding you and trying to accommodate you in this discussion. I've also put effort into giving you explanations that are easily accessible. If I do not feel you reciprocate this with regards to the last reply I sent you, then I will stop trying.

Essentially, I was looking for a reply to:

Call the set of all sets X. Call any set that is not X, a Y. X contains all Ys plus itself. Every set Y is a member of X. Show me how this is contradictory.

Which axiom do you claim is false? — TonesInDeepFreeze

The above which I have underlined. The best that I can see from your last reply as addressing the underlined is:

As long as we have taking of subsets, the inconsistency comes with the assumption that there is a set of all sets. — TonesInDeepFreeze

Then there is an issue in the manner in which you take subsets. Call any set that is not the set of all sets a V', call any set that is not a member of itself a -V, call any set that is simply a set a V.

Can you have a -V as the V of all -Vs? No. Can you have any V as the V of all -Vs? If by a V of all -Vs you mean a V that encompasses ALL -Vs and no other Vs, then you are asking for a -V as the V of all -Vs (in which case what you are asking for is contradictory). But where you are not asking for a -V as the V of all -Vs, then the V of all Vs is such that it encompasses all -Vs, and it is not a -V (because it is a member of itself). -V is only meaningful in the context of the V of all Vs. -V' (any non-set-of-all-sets set that is not a member of itself) is only meaningful in the context of the V' of all V's.

Either we say:

A) There is the V of all Vs. It encompasses all Vs. All other Vs are -Vs in this context.

Or

B) There is the V of all -Vs. It encompasses all -Vs. It is not a -V because it is a V.

If you think a V of all Vs is contradictory, then fine, but then you cannot say a V of all -Vs is contradictory. Do you see? You cannot reject both A and B and be consistent at the same time. It's either A or B. But to my understanding, you reject both A and B.

That is false.

https://thephilosophyforum.com/discussion/comment/546798 — TonesInDeepFreeze

You're posting a reply to another person. Do you not see that you have hurled insults at me accusing me of not giving you proof and suggesting that you gave me proof and then provide a link to something that you said to someone else? Do you not see the problem with this?

In any case, I checked the link (in an attempt to be charitable). I am neither rejecting a set that is a member of itself, nor a set that is not a member of itself. I am rejecting the rejection of the set of all sets. I suggest you read the OP carefully.

AGAIN, you have not shown that "there does not exist a set of which all sets are a member" is contradictory. — TonesInDeepFreeze

It is in the definition of the semantic of "set" that you can have a set of ALL things of which you can have more than one of. Examples of such things include: Numbers, people, shapes, trees, sets. If you can have more than one set, you can have a set of all sets. It is clearly contradictory to say: You can have more than one X, but there's no such thing as a set of all Xs.

I refer to axioms and inference rules — TonesInDeepFreeze

That which you described to me as an axiom I showed as being false. You have not addressed this. Again:

You said: By the axioms, there is no set x such that every set y is a member of x.

To which I replied: Call the set of all sets X. Call any set that is not X, a Y. X contains all Ys plus itself. Every set Y is a member of X. Show me how this is contradictory.

To which you replied: AGAIN, you have not shown that "there does not exist a set of which all sets are a member" is contradictory.

To which I will repeat the last part of the beginning of this post again: It is contradictory to say you can have more than one X, but there's no such thing as a set of all Xs.

You have yet to address that which I have underlined for you. I have addressed the "axiom" which you present as an objection to the set of all sets.

Bear in mind that it was me who suggested that we agree to disagree, to which you decided to hurl insults at me, but still decided to provide your "axiom" as a refutation of the set of all sets.

Defining something into existence is frivolous, but I will play along. — Fooloso4

You don't define something into existence. You simply acknowledge the existence of that which perfectly exists. You don't define something into being triangular. You simply acknowledge the triangularity of that which is perfectly triangular.

Since nothing constrains God's existence there is nothing to prevents the existence of an infinite numbers of Gods. — Fooloso4

You cannot have more than one existence. For you to have more than one existence, non-existence would have to separate one existence from the other. Non-existence existing is contradictory. Thus you cannot have more than one existence.

You cannot have more than one perfect being because you cannot have more than one omnipresent or omnipotent being (both omnipresence and omnipotence are semantical components of being perfect, just as interior angles adding up to 180 degrees is a semantical components of being triangular).

It is only meaningless if you begin by defining God as perfect. — Fooloso4

You define something other than God as a perfect being/existent without running into contradictions (if you are meaningfully/semantically able to), and you will have proven the following wrong:

Only God (the infinite, omnipresent, omnipotent, omniscient, omnibenevolent towards good, omnimalevolent towards evil) is truly perfect (or exists perfectly).

Consider three sets A, B, C that do not contain themselves. There are a lot of such sets, but let's suppose these three are all of them. — tim wood

Ok.

Consider set D defined as the set of all sets that do not contain themselves. — tim wood

Ok, so that means that D necessarily contains A, B, and C.

That is, D contains A, B, C. D is certainly a set. — tim wood

Ok.

And D does not contain itself. — tim wood

D not containing itself or not being a member of itself is a contradiction because you said:

Consider three sets A, B, C that do not contain themselves. There are a lot of such sets, but let's suppose these three are all of them.

If A, B, and C are ALL of them, then by definition, D is a member of itself because D is the set that contains ALL sets that do not contain themselves. D can only be such a set if it contains itself (and it does).

You cannot have a set of all sets that are not members of themselves that is itself not a member of itself. This does not mean that the set of all sets is contradictory. Rejecting the set of all sets is blatantly contradictory. It is the last thing western philosophers should have done with regards to being sincere to the semantic of "set". I reckon because this has gone on for a 100 years, it has become a fierce dogma.

The idea of perfection then can, and in fact does, arise from imperfection. — Fooloso4

I'm not sure how you came to this conclusion. The OP shows that God's non-existence is as semantically/meaningfully contradictory as a perfect triangle's non-triangularity.

By the axioms, there is no set x such that every set y is a member of x.

That's not childishness; it's axiomatic mathematics. — TonesInDeepFreeze

You have not proven this. You have just stated it. Here's my response:

Call the set of all sets X. Call any set that is not X, a Y. X contains all Ys plus itself. Every set Y is a member of X. Show me how this is contradictory.

Again, you are defending a contradiction. That contradiction being "there is no set of all sets". Consider that it is you who is being dogmatic and not me. Who is possibly dogmatic here? The one that is defending a contradiction, or the one that is against it?

I don't know what you think the operative meaning of that is. In any case, when you post nonsense and misinformation, I will decide for myself whether to rebut it. — TonesInDeepFreeze

If I say I did x, and you say I did not do x, and neither of us changes his position, this means that we agree to disagree on this. I hope that's clear to you now.

(1) Set theory is incomplete, therefore set theory is consistent. — TonesInDeepFreeze

If that's what you want to believe, then believe. Rejection of the set of all sets is blatantly contradictory. I say I have provided proof, you say I have not, except you accuse me of arrogance but seem to not apply it to yourself. This is despite the fact that you are defending a contradiction.

There is plenty in this world to be angry and frustrated about. Your ignorant, arrogant, stubborn dogmatism is hardly one of them. — TonesInDeepFreeze

You are like child in your reasoning and manner of discussion. I shouldn't have to spoon-feed you, but they say feeding the needy is good, and per the dictates of pure reason, Karma is real (I've provided proof of this in another thread).

The list of all lists lists itself. In this list, one item is a member of itself whilst all other items are not members of themselves (precisely because they are members of it, and the reference is it).

By definition, the set of all sets encompasses all sets. This includes itself. Thus in the context of sets, the set of all sets encompasses all sets that are not members of themselves, as well as itself. Because it encompasses itself, it is a member of itself. Because all other sets are encompassed by it, they are members of it, and not themselves. This is when the reference is sets (as opposed to lists).

If you directly show a contradiction in the above, I might reply to you. If not, I'm done trying to spoon-feed you. You are in need because your belief system is contradictory, yet you act like you are not, and you complain about the world like some spoilt child (you set these standards for discussion. I am reciprocating). You are contradictory/unreasonable/inconsistent. I suggest you reconcile.

I see your argument. What would you say to the following:

The list of all lists, lists all lists (including itself). So this list contains itself as an element. So this list is a member of itself. Do you agree?

Call the list of all lists L. L = L. Given my interpretation of your argument, it's not the case that L = {L}.

So I don't think it's a case of {N} doing something to N. I think it's a case of N being N and N being such that it contains itself as an element (like the list of all lists).

I strongly recommend you have a read of this:

http://philosophyneedsgods.com/2021/05/22/the-solution-to-russells-paradox-and-the-absurdity-of-more-than-one-infinity/

Thanks for starting this thread. — TheMadFool

You're welcome.

Thus, a set N such that N = {N} can't exist. In other words, no set can contain itself and so Russell's paradox is a none issue. — TheMadFool

I think I get what you're saying, and I recognise that what you say holds true when N is finite. But when N is not finite, what you say does not hold true:

Imagine having four folders on your computer. These are folders '1', '2', '3', and 'all folders on this computer'. The last folder must contain itself in order to meaningfully qualify as a folder of all folders on this computer.

If it is the case that when you open 'all folders on this computer', you get the following folders: '1', '2', '3', and 'all folders on this computer', and then you click the last folder from these four folders and you again get the following folders: '1', '2', '3', and 'all folders on this computer', and you do this again and again forever and this holds true, then arguably the folder 'all folders on this computer' contains itself.

But you're looking at this from a metaphysical perspective (in which case the computer at hand would have to be non-finite because a finite computer does not have the capacity to really contain a folder that contains itself, because it does not have endless energy or potential, and endlessness is needed to sustain a self-containing folder as discussed in the previous paragraph).

I'm approaching this from a purely logical angel:

A) Assume that the letters a-z were representative of all sets that are not members of themselves. You cannot have a set of all sets that are not members of themselves: How are you going to logically write this? a = {a b c...} Here, a is a member of itself. Whatever letter you choose from a-z, it will be a member of itself, so it can't be a set that is not a member of itself.

B) Now assume that the letters a-z were representative of all sets that are members of themselves. You cannot have a set of all sets that are members of themselves: How are you going to logically write this? a = {a b c...} Here, a is a member of itself twice (and whatever letter you choose from a-z, this problem will occur), and such a thing is as contradictory as a set that is not a member of itself, that is in fact a member of itself (as highlighted in A).

Do you see how B is the overlooked part of Russell's paradox?

Yes, you are refusing to discuss - refusing to acknowledge that your argument does not work. We are not agreeing to disagree, you are running away, ok? No agreement. You. Running. Away. — Bartricks

How you interpret your empirical experiences, is your responsibility. It is not my concern.

I refuse to agree with you. I don't see you as having a choice in this matter. This is why I suggested that we agree to disagree. If I choose to disagree with you and you do not choose to agree with me, then we either agree to disagree, or we continue to discuss. But I am refusing to continue to discuss.

ZF has not been shown to be inconsistent. And lack of comprehensiveness does not imply inconsistency. — TonesInDeepFreeze

ZF implies incompleteness in proof, theory or system. Perhaps some are happy with such standards, I am not.

In any case, your last reply to me suggests that it's a waste of time to continue this discussion with you. Also, the post that followed it suggests that you are upset, angry, or frustrated, which is not a good state to be in when discussing matters of logic or pure reason. I presented what I say is clear proof, you say that I have not. This has happened twice now, there's no point in there being a third time. I think we should just agree to disagree.